Graphical models use Markov properties to establish associations among dependent variables. To estimate spatial correlation and other parameters in graphical models, the conditional independences and joint probability distribution of the graph need to be specified. We can rely on Gaussian multivariate models to derive the joint distribution when all the nodes of the graph are assumed to be normally distributed. However, when some of the nodes are discrete, the Gaussian model no longer affords an appropriate joint distribution function. We develop methods specifying the joint distribution of a chain graph with both discrete and continuous components, with spatial dependencies assumed among all variables on the graph. We propose a new group of chain graphs known as the generalized tree networks. Constructing the chain graph as a generalized tree network, we partition its joint distributions according to the maximal cliques. Copula models help us to model correlation among discrete variables in the cliques. We examine the method by analyzing datasets with simulated Gaussian and Bernoulli Markov random fields, as well as with a real dataset involving household income and election results. Estimates from the graphical models are compared with those from spatial random effects models and multivariate regression models. / Graduation date: 2013
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/33644 |
| Date | 16 August 2012 |
| Creators | Che, Xuan |
| Contributors | Gitelman, Alix I. |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
Page generated in 0.0018 seconds